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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p><dfn class="terminology">Useful Expansions</dfn>   Some power series expansions about 0 that you should be familiar with.Except for the last one, the expansions are valid for all <span class="process-math">\(z\)</span> (i.e. the radius of convergence is <span class="process-math">\(\rho=\infty\)</span>).</p>
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\begin{equation*}
e^z=\sum_{n=0}^{\infty}\frac{z^n}{n!}
\end{equation*}
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\begin{equation*}
\cos(z)=\sum_{k=0}^{\infty}(-1)^k\frac{z^{2k}}{(2k)!},\quad \sin(z)=\sum_{k=0}^{\infty}(-1)^k\frac{z^{2k+1}}{(2k+1)!}
\end{equation*}
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\begin{equation*}
\textcolor{red}{\frac{1}{1-z}=\sum_{n=0}^{\infty}z^n}~~~~(|z|&lt;1)
\end{equation*}
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